Problem: The equation of a circle $C$ is $x^2+y^2-18y+45 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2) + (y^2-18y) = -45$ $(x^2) + (y^2-18y+81) = -45 + 0 + 81$ $x^2 + (y-9)^{2} = 36 = 6^2$ Thus, $(h, k) = (0, 9)$ and $r = 6$.